Calculating device

ABSTRACT

A calculating device for making mathematical computations constituted by a sleeve member, an endless belt and a slide member. There are longitudinally extending mathematical scales on both the sleeve member and the belt and the belt is trained around the ends of the slide member to form an assembly which is telescopically slidable into the sleeve. There are slots in the sleeve alongside the sleeve mathematical scale with which the belt scale comes into registry when the slide/belt assembly is within the sleeve. A computation based on the relationship z f(x,y) may be made by setting x1 on the belt mathematical scale adjacent the identity operator on the sleeve mathematical scale and reading z1 on the belt scale adjacent y1 on the sleeve scale.

[451 lm1g.1,1972

United States atet Schwarz et ah.

- Primary Examiner-Stephen J. Tomsky [54] CALCULATING DEVICE [72] Inventors: Walter lK. Schwarz; David J.

Schlink both of Peoria I". Attorney-Koenig, Sennmger, Powers & Leavitt OOOO @wOOb PATENERUB i I9?? SliE I E! UF I3 IOW 'Ib C: a2000 oooooc 34000 OOOZZ OOOLl OOOVS v 00091 220000 V :f 050000 oooll 900000 950000 Docol 1000000 BACKGROUND OF THE INVENTION This invention relates to calculating devices and,

more particularly, to a device for making linear conversions such as currency conversions. In the course of both business and pleasure, it is often necessary to convert various quantities from one unit to another. Through this type of conversion is routine in the office or shop, it can be an aggravating nuisance to a person without ready access to paper and a writing surface or office calculating equipment. Such inconveniences particularly aftlict the traveler visiting a foreign country, who is everywhere faced with the question of what amount of American currency is equivalent to amounts of foreign currency representing the price of goods and services essential to his travel or his mission.

Though a multitude of calculating devices are availa- I ble for making linear conversions, many of these are too heavy or bulky t'o be conveniently portable. One calculating device which is readily portable is a small slide rule. Linear conversions can be quite readily carried out on a slide rule. However, when a slide rule is used to convert a quantity from one unit to another, only the significant figures of the quantities are indicated on the rule. The individual making the conversion is then faced with the mental task of locating the decimal point himself. Location of the decimal point in a linear conversion problem is usually an elementary matter, but even the most intelligent of men may be prone to error in this regard when the conversion must be made quickly on short notice.

SUMMARY OF THE INVENTION Among the several objects of the present invention, therefore, may be noted the provision of means by which mathematical computations may be simply and readily accomplished; the provision of a calculating device for making linear conversions; the provisions of such a device which is light, compact and easily portable; the provision of such a device whereby the decimal point of the amount in the converted units may be readily determined; and the provision of such a device by which an amount in one currency may be readily converted to an equivalent amount in a variety of other currencies.

Briefly, the present invention is directed to a calculating device for making mathematical computations, comprising an elongate slide member, an endless belt, and a sleeve member. The endless belt has a circumference slightly greater than the sum of twice the length plus twice the thickness of the slide member and is trained around the ends of the slide member, being movable therearound. A mathematical scale on the endless belt extends longitudinally thereof. The sleeve is formed for a telescopic sliding fit therein of the slide member and belt assembly so that the assembly may slide lengthwise within the sleeve member. The sleeve member also has an elongate longitudinally extending slot'in registry with the belt mathematical scale when the slide member and belt assembly is within the sleeve member and a mathematical scale having an identity operator index alongside the slot. The sleeve mathematical scale has a unit dimension which is the same as the unit dimension of the belt mathematical scale. Thus a computation based on the relationship z =f(x,y) may be made by setting x, on the belt mathematical scale adjacent the identity operator on the sleeve mathematical scale and reading zl on the belt scale adjacent y, on the sleeve scale.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. l is a plan view of a preferred embodiment of the present invention;

FIG. 2 is a broken sectional view along the line 2-2 of FIG. l;

FIG. 3 is a sectional view along the line 3--3 of FIG.

FIGS. 4 and 5 are plan views on a smaller scale showing the two faces of the slide member of the device shown in FIG. l; and

FIG. 6 is a developed view on a smaller scale of the endless belt member included in the device shown in FIG. l.

Corresponding reference characters indicate cor responding parts throughout the several views of the drawings DESCRIPTION OF THE PREFERRED EMBODIMENTS i By use of the calculating device to the present invention, linear conversions or other mathematical computations may be quickly, confidently, and accurately made. The invention embodies a unique combination of sleeve, belt and slide, each bearing indicia whose relative orientation may be varied to make essentially any linear conversion or other simple mathematical computation. In its preferred form, the calculating device of the invention is compact, light-weight and portable and, in a particularly preferred form, provides for the definitive location of the decimal point of the product of a given linear conversion, being in this respect particularly superior to a conventional slide rule.

Referring to FIG. l, there is shown a sleeve member 1 having on one face thereof (its front face) two parallel logarithmic scales 3a and 3b. Scale 3a and 3b is one cycle, with the range of each scale being slightly greater than one-half cycle. One cycle on a logarithmic scale includes all numbers lying between two numbers whose base l0 logarithms differ by 1.0000. Corresponding values on the scales 3a and 3b are longitudinally staggered from one another and the ranges of the scales overlap slightly. Elongate slots 5a and 5b constituting windows in sleeve 1 extend longitudinally alongside scales 3a and 3b, respectively. An endless belt 7 is trained around an elongate slide 9 constituted by a rectangular card to form an assembly which is adapted to slide telescopically within sleeve member l. The circumference of endless belt 7 is slightly greater than the sum of twice the length plus twice the thickness of slide member 9 so that the belt fits snugly around the slide yet is movable therearound by finger pressure. The relationship of slide 9 to belt 7 to sleeve 1, when the calculating device is assembled, is shown in FIG. 2.

Parallel logarithmic scales lla and 11g are so located on the belt as to be in registry with slots 5a and 5b respectively, when the slide and belt assembly is within sleeve member 1. Scales 11a and 1lb have the same unit dimensions as scales 3a and 3b and are staggered relative to each other a longitudinal distance corresponding to the longitudinal distance by which scales 3a and 3b are staggered. Thus, as the drawing indicates, when 310 on the scale 3a is aligned with 80000 on the scale 11a, the same two numbers are aligned on scales 3b and 11b, respectively. The total range of scales 11a and 11b is two cycles, with the range of each being slightly greater than 11,@ cycles. These ranges assure that, when a linear conversion is carried out on the device in the manner described below, the product of the conversion always appears on the belt scale in a position where it can be read through slot a or 5b.

To make a linear conversion, the conversion factor for converting a quantity in a first unit to a quantity in a second unit is set'adjacent unity index U on scale 3a. The quantity in the second unit is then read on either scale l la or 1lb adjacent the corresponding quantity in the first unity on scale 3a or 3b.

Though the preferred embodiment of the present invention is a device having logarithmic scales, and is consequently adapted for making linear conversions, other mathematical scales can be substituted for the logarithmic scales to transform the device onto one adapted for other types of computations. Thus, for example, if linear scales are employed, the device may be used for simple addition and subtraction; or, if square root scales are used, the device may be utilized to find the length of the hypotenuse of a right triangle. Provided that the arrangement of numbers on sleeve and belt scales both correspond to a particular mathematical function, and have the same unit dimension, the

' device can be used for making calculations related to that function. This is the meaning of theterm mathematical scale as used herein.

The operation of the device, as described above is essentially one of adding lengths on the scales of the device. In the preferred embodiment of the invention, where logarithmic scales are used, the adding of lengths corresponds to the adding of logarithms and the operation is one of multiplication. Thus, if the multiplier on the belt scale set adjacent the unity index on the sleeve scale is defined as x the multiplicand on the sleeve scale is defined as y1, and the product on the belt scale read adjacent y1 is defined as zi, the computation is simply zl xl-yl. If a linear scale is used on the other hand, z1=x1 y1. Ifa square scale is used, zl Ji, -l-

Nlyl, 2. If a square root scale is used, the relationship is z, xl 2 y1 2. Generally, therefore, mathematical computations of the type z f (x, y) can be made using the device of the invention with the nature of the functional relationship of z to x and y depending on the mathematical arrangement of x and y on the belt and sleeve scales, respectively.

To add the lengths corresponding to x, and y 1 and accurately obtain zl where z =f(x,y), it is evident that the index number on the sleeve scale (defined, e.g., as yo), adjacent which x1 is set in making a computation, must be a number which converts x1 to x1 according to the function z =j(x,y). Thus, in the case of linear conversions, this number (U in FIG. l) is unity (1.0000. so that xl'l =x,. In addition, on the other hand, this index number must be 0 so that x1 -l- 0 =x1. Genetically, this index number is referred to as the identity operator, i.e., that number which leaves unchanged every element in the domain of the function.

With regard to the construction of the calculating In a preferred form of the invention, endless belt 7 is transparent and slide member 9 is of substantially the same length as sleeve member l. The slide member is provided with an index 13a lying-directly underneath belt scale 11a and spaced from one end of the slide member by a distance corresponding to the distance that unity index U on sleeve scale 3a is spaced from the corresponding end of sleeve member l. This arrangement facilitates aligning the conversion factor on scale lla with unity index U on scale 3a. Thus, the slide/belt assembly is removed from the sleeve, and belt 7 is rotated around slide 9 until the conversion factor is in registry with index 13a. The slide/belt assembly is then returned to the sleeve and adjusted so that neither end of the assembly protrudes from an end of the sleeve. As a result of the distance and dimension relationships referred to above, this assures that the index on the slide and consequently the conversion factor on the belt is aligned with unity index U on the sleeve.

In a particularly preferred embodiment of the invention, endless belt 7 is transparent as above noted and decimal point locating indicia are provided for 23B, the sleeve and belt logarithmic scales. Indicia 15A and 15B for the sleeve scales are superimposed on the scales themselves while the indicia forthe belt scales are located on the underlying slide. The latter indicia are more clearly illustrated at 17A, 17B, 19A, 19B, 21A, 21B, and 23A, 23B in FIGS. 4 and 5, 17A and B and 19A and B being on one face of the slide, and 21A and B and 23A and B being on the other. Each of these four diferent sets of indicia is adapted to be in registry with slots 5a and 5b when sleeve 1 and slide 9 are in aparticular orientation relative to one another. Indices 13b, 13C, and 13d serve the same function as index 13a when indicia 19A and B, 21A and B, and 23A and B, respectively, are in registry with slots 5a and 5b. The nature a function of the decimal point locating indicia shown in FIGS. 4 and 5 are set forth below.

There are two principal obstacles to providing for ready location of the decimal point in the product of linear conversion by the user of a calculating device. First, if conventional decimal points or their equivalents are included on a given scale, their location on that scale is normally fixed and the range of the scale is thereby limited to a particular cycle corresponding to the numbers between two particular integral powers of l0. Second, the decimal point location in the product is often different from the decimal point location in either the multiplier or the multiplicand. Thus, even if alternative locations of the decimal point are provided on all the scales of the device, the user is still presented with his original problem, i.e., determining which of the alternative decimal point locations is correct for the product.

The decimal point locating indices 15A and B, 17A and B, 19A and B, 21A and B, and 23A and B overcome the first of the above two obstacles. Each of these indices is constituted by a set of differently colored stripes located side-by-side. As shown, each of sets 23A and 23B comprises two stripes designated a and b, which may be red and blue, respectively. Each of the other sets comprises three stripes designated a, b and C. As to sets A and B, a is shown as red, b as blue, and C is white for the better legibility of the 3a and 3b scale markings thereon. As to sets 17A and B, 19A and B and 21A and B, a is red, b is blue and cis black. In each set, the outside line of stripe a is designated m, the line between stripes a and b is designated n, and the line at the outside of b in sets 23A and B and the line between stripes b and c in the other sets is designated p.

The color-coding does not, of itself, resolve the problem of locating the decimal point in the product. However, by having the left-hand edge of the left-hand stripe between the first and second significant figures on scales 3a and 3b, a preferred embodiment of the calculating device of the present invention is adapted for simple and accurate location of the decimal point. The operation by which the decimal point in the product is located may be conveniently illustrated by defining longitudinal edge m of each set of indices as the 10 position, edge n as the 10 position, and edge p as the l02 position, et cetera.

Provided that at least one of the multiplier factor on the belt scale and the multiplicand factor on the sleeve scale has its decimal point in the 10 position, the location of the decimal point in the product on the belt scale is the same as the rightmost decimal point location of its two factors. Thus, if the decimal points in both the multiplicand and multiplier are in the l00 position, the decimal point location in the product is also in the 100 position. If the decimal point location in the multiplier or multiplicand is in the 10l position, the decimal point in the product is also in the 10l position. Similarly, if the decimal point is in the 102 position in one of the two factors, the decimal point is in the l02 position in the product.

As the device of the invention has been so far described, the range of linear conversions in which the decimal point may be easily located remains somewhat limited. Thus, for simple correspondence to exist between the decimal point position in the product and the rightmost decimal point position in one of its factors, the decimal point location in the other factor must be in the 100 position. If neither of the factors has its decimal point in the l00 position, the decimal point in the product may still be determined, of course, as those skilled in the art will recognize. In such case, the exponent of the position designation of the decimal point in the multiplier is added to the exponent of the position designation of the decimal point in the multiplicand to give the exponent of the position designation of the decimal point in the product. Thus, if the decimal points in both the multiplier and multiplicand are in the 101 position, the decimal point in the product is in the 102 position. Location of the decimal point in this manner can be a confusing problem, however, especially for the traveler who must make quick conversions of currency, for example, on short notice.

In the preferred embodiment of the invention, therefore, a number of alternative locations of the l00 position are provided for the belt scale, allowing conversion of a wide range of multiplicands on the sleeve scale by a wide range of multipliers on the belt scale without the need for adding exponents. In this embodiment slots 5a and 5b are located unequal distances from the longitudinal center line of sleeve l, with the distance between the center line of slot 5a and the center line of the sleeve differing sufficiently from the distance between the center line of slot 5b and the center line of the sleeve that entirely different areas of slide 9 and belt 7 are brought into registry with said slots when the lengthwise orientation of the slide/belt assembly to sleeve is reversed. This allows the two separate sets of decimal point locating indicia 17A and B, 19A and B, 211A and B, and 23A and B to be placed on each side of slide 9, as indicated in FIGS. 4 and 5. The l00 position in each of these four sets of indicia defines a different order of magnitude for the quantity on the belt scale. Thus, for example, the l00 position on scale 17A and B may define an order of magnitude of 0.1 to 1.0, scale 19A B an order of magnitude of 1.0 to 10.0, scale 21A and B an order of magnitude of 10.0 to 100.0, and scale 23A and B an order of magnitude of 100.0 to 1,000.0.

It will be recognized, of course, that belt scales lla and 1lb can be used with sleeve scales 3a and 3b only when the lengthwise orientation of the slide/belt assembly is such that scales lla and 1lb run in the same direction as scales 3a and 3b. This condition is met in only two of the four possible orientations of the slide/belt assembly to the sleeve. To make use of the extra two decimal point locating indicia, for example, 19A and B and 21A and B, two additional belt scales 25a and 25b are provided. Scale 25a is located alongside scale 1lb and extends in the opposite direction from it (see FIG. 6). By orienting the slide/belt assemblies such that scales 25a and 25b extend in the same direction as scales 3a and 3b, scales 25a and 25b, along with decimal point locating indicia 19A and B and 21A and B, come into registry with slots 5a and 5b.

The embodiment of the invention shown in the drawings is a currency converter. The ratio of foreign currencies to U.S. dollars ranges from less than one for the Russian ruble to over 600 for the Italian lira or the Japanese yen. To make currency conversion calculations, the conversion ratio is set adjacent the unity index on sleeve scale 3a and an amount in the foreign currency is read on belt scales 11a, 1lb, 25a or 25b adjacent the equivalent amount in U.S. dollars on sleeve scales 3a or 3b. If the conversion ratio of foreign currency is less than one, the slide/belt assembly is oriented in the sleeve l so that decimal point locating indicia 17A and B (designated A in FIG. 4) are in registry with slots 5a and 5b. Indicia 17A and 17B are so located on slide 9 that the edge m of the stripe is located immediately to the left of the first significant numerals on the belt scale. Thus a range of multipliers in the range between 0.1 and 1.0 are established on the belt scale and the decimal point location of any product on the belt scale will be the same as the location of the decimal point in the multiplicand read from the sleeve scale. Similarly, decimal point locating indicia 19A and 119B, 211A and 211B, and 23A and 23B are arranged for corresponding location of the decimal point in multiplicand and product where the conversion rate is between 1.0 and 10.0, 10.0 and 100.0, and 100.0 and 1,000, respectively. These indicia are designated B, C,

and D, respectively, in FIGS. 4 and 5. Thus, by orienting the slide belt assembly so that indicia 19A and B are in registry with slots 5a and 5b, currencies such as Brazilian new cruzeros (3.2 to l), Canadian dollars (1.08 to l), Danish krone (7.44 to l), French francs (4.89 to l), West German deutsch marks (4.00 to l), Netherland guilders (3.60 to l) and Swiss francs (4.32 to 1) can be directly correlated to equivalent amounts of U.S. dollars. By orienting the slide belt assembly so that indicia 21A and B are in registry with slots 5a and 5b, direct conversions can be made between U.S. dollars and currencies such as Austrian schillings (25.78 to 1 Belgian francs (49.60 to l Greek drachmas (29.85 to l), Hungarian forints (30.03 to l), Mexican pesos (12.49 to 1) and Spanish pesetas (69.60 to l). And finally by orienting the slide scale assembly so that indicia 23A and B are in registry with slots 5a and 5b, direct conversions can be made between U.S. dollars and Japanese yen (631.00 to 1) or Italian lira (623.00 to l).

By way of example 5 U.S. dollars are converted to an equivalent amount of Austrian schillings in the following fashion. Because the conversion ratio of schillings to dollars is 25.78, a number between l and 100, the slide/belt assembly is oriented within the sleeve so that decimal point locating indicia 21A and B are in registry with slots Sa and b. Before the slide/belt assembly is inserted into the sleeve, the conversion ratio of 25.78, on belt scale lla or 25a, is brought into registry with index 13C. As points corresponding to significant figures 2578 appear in both the first full cycle and the second half cycle on scales lilla and 25a, it is important to be certain that the point on the belt scale brought into registry with the index 13C is a point on the first cycle of the belt scale. This can be readily checked by ascertaining that the l00 position, i.e., edge 21A m of the decimal point locating indicia 21A appears between the second and third significant figures on the belt scale.

There is, of course, no line on the scale which directly corresponds to the significant figures 2578. The point corresponding to these figures must be interpolatively estimated. Such estimation dictates that the index 13C be brought into registry with a point slightly past the mid-point between the lines corresponding to the significant figures 2550 and 2600, respectively.

After the conversion factor is properly aligned with index 13C, the slide belt assembly is inserted in the sleeve and positioned so that index l3t` is aligned with unity index U. An amount in Austrian schillings corresponding to any amount between l and 1,000 U.S.

dollars may now be read on the belt scale adjacent the quantity in dollars to which it is equivalent. The decimal point location of the quantity in schillings corresponds directly to the decimal point location of the quantity in dollars. Thus, taking the decimal point location the 100 position, it may be seen that 5 U.S. dollars are equivalent to approximately 129 Austrian schillings. Taking the decimal point in the l01 position, 50 dollars are seen to be equivalent to about 1,290 schillings, and so on.

Though the principal emphasis in the above discussion has been on the conversion of dollars to schillings, conversions from schillings to dollars can be made with equal facility. If, for example, it is desired to determine the dollar equivalent of 60 schillings this is accomplished by simply reading the equivalent quantity in dollars on sleeve scale 3a, i.e., about $2.32, adjacent 60 on the belt scale. Taking the decimal point in the l0l position it can be seen that 600 schillings is equivalent to $23.20 and taking the decimal point in the l02 position that 6,000 schillings is equivalent to $232.00.

FIG. 3 illustrates a preferred construction for the device. The sleeve member is preferably constituted by a rectangular sheet of rigid transparent plastic which is folded to form a front wall 27 and a back wall 29 of the sleeve, joined by relatively narrow side walls 3l and 33. One end of the plastic sheet laps the other end of the sheet at an area along the back wall as shown at 35. A panel 37 of opaque material such as paper, having sleeve scales 3a and 3b printed thereon, adheres to front wall 27 of sleeve l, preferably to the inside surface thereof. Elongate openings in the panel define slots 5a and 5b. Endless belt 7 is constituted by a thin film of flexible transparent material such as the polyester film sold under the trade designation Mylar by E. I. DuPont deNemours and Company, Inc. Slide member 9 is constituted by a thin rectangular sheet of relatively rigid material such as plastic or cardboard. Cardboard having a very thin surface lamination of transparent plastic is a particularly suitable material for slide member 9. According to the above construction a pocket size calculating device can readily be made which is both light in weight and durable.

In view of the above, it will be seen that the several objects of the invention are achieved and other advantageous results attained.

As various changes could be made in the above constructions without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1l. A calculating device for making mathematical computations comprising an elongate slide member, an endless belt having a circumference slightly greater than the sum of twice the length plus twice the thickness of the slide member, said belt being trained around the ends of said slide member and being movable therearound, a mathematical scale on said endless belt extending longitudinally thereof, a sleeve formed for a telescopic sliding fit therein of said slide member and belt assembly so that said assembly may slide lengthwise within the sleeve member, said sleeve member also having an elongate longitudinally extending slot in registry with said belt mathematical scale when said slide member and belt assembly is within the sleeve member, a mathematical scale having an identity operator index on the sleeve member alongside said slot, said sleeve mathematical scale having the same unit dimension as said belt mathematical scale, whereby a computation based on the relationship z f(x,y) may be made by setting x1 on the belt mathematical scale adjacent the identity operator on the sleeve mathematical scale and reading zl on the belt scale adjacent yl on the sleeve scale.

2. A calculating device as set forth in claim l wherein said endless belt is transparent and said slide member is of substantially the same length as said sleeve member,

said slide member having an index at a position directly underneath said belt scale spaced from one end of said slide member a distance corresponding to the distance that the identity operator index on the sleeve scale is spaced from the corresponding end of said sleeve member.

3. A calculating device as set forth in claim 1 having a second mathematical scale on the belt parallel to the first belt scale, a second elongate slot in said sleeve member parallel to the first slot, the second slot being in registry with the second belt scale when the slide member and endless belt assembly is within the sleeve member, and a second mathematical scale on the sleeve alongside said second slot, the second belt scale and second sleeve scale each having the same unit dimensions as the first belt scale.

4. A calculating device as set forth in claim l wherein said scales are logarithmic scales and said identity operator index is a unity index whereby a quantity expressed in a first unit may be converted to a corresponding quantity expressed in a second unit by setting a conversion factor on the belt logarithmic scale adjacent said unity index on the sleeve logarithmic scale and reading the quantity in the second unit on the belt scale adjacent the corresponding quantity in the first unit on the sleeve scale.

5. A calculating device as set forth in claim 4 wherein said endless belt is transparent and said slide member is of substantially the same length as said sleeve member, said slide member having an index at a position directly underneath said belt scale spaced from one end of said slide member a distance corresponding to the distance that the unity index on the sleeve scale is spaced from the corresponding end of said sleeve member.

6. A calculating device as set forth in claim 5 having coded decimal point locating indicia on said sleeve scale and corresponding coded decimal point locating indicia on said slide member underneath said belt scale.

7. A calculating device as set forth in claim I wherein said sleeve member is constituted by a rectangular sheet of rigid transparent plastic folded to form a front wall and a back wall of said sleeve joined by relatively narrow side walls with one end of said sheet lapping the other end of said sheet at an area along said back wall, a panel of opaque material having said sleeve scale lll thereon adhering to aid front wall with elongate 9. A calculating device as set forth in claim 6 having l a second logarithmic scale on the belt parallel to the first belt scale, a second elongate slot in said sleeve parallel to said first slot, the second slot being in registry with the second belt scale when the slide member and endless belt assembly is within the sleeve member and a second logarithmic scale on the sleeve alongside the second slot, t e second belt and second slefeve scales each having t e same unit dimensions as the irst belt scale.

10. A calculating device as set forth in claim 9 having a third logarithmic scale on the belt alongside the first belt scale extending in the DIRECTION OPPOSITE THEREFROM AND HAVING A FOURTH LOGARITHMIC SCALE ON THE BELT ALONG- SIDE SAID SECOND BELT SCALE EXTENDING IN THE DIRECTION OPPOSITE THEREFROM, SAID THIRD AND FOURTH BELT SCALES BEING IN REGISTRY WITH SAID SLOTS WHEN THE SLIDE MEMBER AND SLEEVE MEMBER ARE ALIGNED SO THAT SAID THIRD AND FOURTH BELT SCALES EXTEND IN THE SAME DIRECTION AS SAID SLEEVE SCALES.

lll. A calculating device as set forth in claim 6 wherein said decimal point locating indicia are constituted by the boundaries between a plurality of adjacent stripes superimposed upon said sleeve scale and located on said slide directly underneath said belt scale, respectively.

12. A calculating device as set forth in claim 11 wherein said stripes are of different colors with corresponding stripes on the slide and the sleeve being of the same colors.

gyggg@ UNITED STATES PATENT oEFIICE CERTIFICATE OF .CORRECTION Patent No. 3,680,775 'Dated August l, 1972 `Inventor(s) Walter K. Schwarz et al.

It is certified that error appears in the above-identified patent and that said LetterszPatent are hereby corrected as shown below:

Column l, line ll, through" should read Though Column 2, line 6A "lla and 11g" should read lla and 1lb Column 3, line I8, "first unity" should read first unit line 23, "onto" should read into line 56, "y l" should read y Column l line 32, "for 23B, the" Should read for bothlthe --5 line 48, "nature a" should read nature and Column 6, line 3A, "scale 1lb" should read Scale'lla and extends in the opposite direction therefrom while the scale 25b is located alongside scale llb". Column lO, line l, "aid" should read said-e; lines 25-35, "DIRECTION OPPOSITE THERE- FROM AND HAVING- Av FOURTH LOGARITHMIC SCALE ON THE BELT ALONGSIDE SAID SECOND BELT SCALE EXTENDING IN THE DIRECTION OPPOSITE THEREFROM, SAID THIRD AND FOURTH BELT SCALES BEING IN REGISTRY WITH SAID SLOTS WHEN THE SLIDE MEMBER AND SLEEVE MEMBER ARE ALIGNED SO THAT SAID THIRD AND FOURTH BELT SCALES EXTEND IN THE SAME DIRECTION AS SAID SLEEVE SCALES." should read -fdirection opposite therefrom and having a fourth logarithmic scale on the belt alongside said second belt scaleextending in the direction opposite therefrom, said third and fourth belt scales being in registry with said slots when the slide member and sleeve member are aligned so that said third and fourth belt scales extend in the same direction as said sleeve scales.

Signed and sealed this' 9thday of January 1973 (SEAL) Attest:

EDWARD M.FLE'I`CHER,JR. l ROBERT GOT'ISCHALK v Attesting Officer Commissioner of Patents gjgfgof STATES PATENT -OFFICE CERTIFICATE OF .CORRECTION Paentm. 3,680,775 hated August 1, 1972 Irwentm-(s) lWalter K. Schwarz etA al.

It; is certified that lerror appears in the above-identified patent and that said LettersPatent are hereby corrected as shown below.:

Column l, line ll, "through" should read Though Column 2, line 614, 'Tlla and 11g" should read lla and llb Column 3, line I8, 4"first unity" should read first unit line 23,- "ont'o" should read vinto --g line 56, "y l should read y Column U., line 32, "for 23B, the" should read for y bothlthe line 48, "nature a" should read nature and Column 6, line 3M, "scale llb" should read scale lla and extends in the opposite direction therefrom while the scale 25h is locatedl alongside scale llb". Column lO, line l, "aid" should read saidl ,-;4 lines 25-35, "DIRECTION OPPOSITE THERE- FROM AND H AVING- A FOURTH LOGARITHMIC SCALE ON THE BELT AL'ONGSIDE SAID SECOND BELT SCALE EXTENDING IN THE DIRECTION OPPOSITE THEREFROIVI, SAID THIRD AND FOURTH BELT SCALES BEING IN REGISTRY WITH SAID SLOTS WHEN THE SLIDE lVIEIVII-S'ER AND SLEEVE MEMBER ARE ALIGNED SO THAT SAID. THIRD AND FOURTH BELT SCALES EXTEND IN THE SAME DIRECTION AS SAID SLEEVE SCALES.n should read -f direction opposite therefrom and having a fourth logarithmic lscale on the belt alongside said second belt scaleextending; in the direction opposite therefrom', said third and fourth belt scales being in registry with said slots when the slide member and sleeve member are aligned so that. said third and fourth belt lscales extend in the same direction as said sleeve scales Signed ana sealed this' sth. day`A of January 1973.

(SEAL) Attest I EDWARD M.FLETCHER,JR. v ROBERT GOTTSCHALK Attesting Officer l v Commissioner of Patents 

1. A calculating device for making mathematical computations comprising an elongate slide member, an endless belt having a circumference slightly greater than the sum of twice the length plus twice the thickness of the slide member, said belt being trained around the ends of said slide member and being movable therearound, a mathematical scale on said endless belt extending longitudinally thereof, a sleeve formed for a telescopic sliding fit therein of said slide member and belt assembly so that said assembly may slide lengthwise within the sleeve member, said sleeve member also having an elongate longitudinally extending slot in registry with said belt mathematical scale when said slide member and belt assembly is within the sleeve member, a mathematical scale having an identity operator index on the sleeve member alongside said slot, said sleeve mathematical scale having the same unit dimension as said belt mathematical scale, whereby a computation based on the relationship z f(x,y) may be made by setting x1 on the belt mathematical scale adjacent the identity operator on the sleeve mathematical scale and reading z1 on the belt scale adjacent y1 on the sleeve scale.
 2. A calculating device as set forth in claim 1 wherein said endless belt is transparent and said slide member is of substantially the same length as said sleeve member, said slide member having an index at a position directly underneath said belt scale spaced from one end of said slide member a distance corresponding to the distance that the identity operator index on the sleeve scale is spaced from the corresponding end of said sleeve member.
 3. A calculating device as set forth in claim 1 having a second mathematical scale on the belt parallel to the first belt scale, a second elongate slot in said sleeve member parallel to the first slot, the second slot being in registry with the second belt scale when the slide member and endless belt assembly is within the sleeve member, and a second mathematical scale on the sleeve alongside said second slot, the second belt scale and second sleeve scale each having the same unit dimensions as the first belt scale.
 4. A calculating device as set forth in claim 1 wherein said scales are logarithmic scales and said identity operator index is a unity index whereby a quantity expressed in a first unit may be converted to a corresponding quantity expressed in a second unit by setting a conversion factor on the belt logarithmic scale adjacent said unity index on the sleeve logarithmic scale and reading the quantity in the second unit on the belt scale adjacent the corresponding quantity in the first unit on the sleeve scaLe.
 5. A calculating device as set forth in claim 4 wherein said endless belt is transparent and said slide member is of substantially the same length as said sleeve member, said slide member having an index at a position directly underneath said belt scale spaced from one end of said slide member a distance corresponding to the distance that the unity index on the sleeve scale is spaced from the corresponding end of said sleeve member.
 6. A calculating device as set forth in claim 5 having coded decimal point locating indicia on said sleeve scale and corresponding coded decimal point locating indicia on said slide member underneath said belt scale.
 7. A calculating device as set forth in claim 1 wherein said sleeve member is constituted by a rectangular sheet of rigid transparent plastic folded to form a front wall and a back wall of said sleeve joined by relatively narrow side walls with one end of said sheet lapping the other end of said sheet at an area along said back wall, a panel of opaque material having said sleeve scale thereon adhering to aid front wall with elongate openings in said panel defining said slots.
 8. A calculating device as set forth in claim 4 having a second logarithmic scale on the belt parallel to the first belt scale, a second elongate slot in said sleeve parallel to said first slot, the second slot being in registry with the second belt scale when the slide member and endless belt assembly is within the sleeve member, and a second logarithmic scale on the sleeve alongside the second slot, the second belt and second sleeve scales each having the same unit dimensions as the first belt scale.
 9. A calculating device as set forth in claim 6 having a second logarithmic scale on the belt parallel to the first belt scale, a second elongate slot in said sleeve parallel to said first slot, the second slot being in registry with the second belt scale when the slide member and endless belt assembly is within the sleeve member and a second logarithmic scale on the sleeve alongside the second slot, the second belt and second sleeve scales each having the same unit dimensions as the first belt scale.
 10. A calculating device as set forth in claim 9 having a third logarithmic scale on the belt alongside the first belt scale extending in the DIRECTION OPPOSITE THEREFROM AND HAVING A FOURTH LOGARITHMIC SCALE ON THE BELT ALONGSIDE SAID SECOND BELT SCALE EXTENDING IN THE DIRECTION OPPOSITE THEREFROM, SAID THIRD AND FOURTH BELT SCALES BEING IN REGISTRY WITH SAID SLOTS WHEN THE SLIDE MEMBER AND SLEEVE MEMBER ARE ALIGNED SO THAT SAID THIRD AND FOURTH BELT SCALES EXTEND IN THE SAME DIRECTION AS SAID SLEEVE SCALES.
 11. A calculating device as set forth in claim 6 wherein said decimal point locating indicia are constituted by the boundaries between a plurality of adjacent stripes superimposed upon said sleeve scale and located on said slide directly underneath said belt scale, respectively.
 12. A calculating device as set forth in claim 11 wherein said stripes are of different colors with corresponding stripes on the slide and the sleeve being of the same colors. 